In the past, thermoformed plastic articles, such as plastic cups generated from a thermoforming line, were stacked by hand as the articles were ejected into a bin from a trim press. At some subsequent point in time, a shaking box was operated by hand to stack the plastic cups. More particularly, an operator loaded plastic cups into the shaking box, after which the operator shook the box to agitate the cups, causing the cups to internest as the relatively narrow, tapered bottom ends tended to nestle into the wider, open-mouthed top ends as a result of the shaking. It was further discovered that, if the height of such a tapered cup was greater than a maximum diameter of such cup, shaking or jiggling of the box would stack the cups together. It was further found that dumping the partially stacked cups from one box into another box further encouraged stacking as the another box was further agitated or shaken. However, the shaking of one or more boxes by hand was found to be relatively inefficient, and tiring for the operator. Furthermore, as an operator becomes tired, it becomes difficult to continue generating sufficient shaking or agitation of the cups. Even furthermore, the number of cups that can be agitated at one time is limited by the strength of the operator and the size of box that the operator can carry and shake as bulk and weight limit the operator's performance when stacking cups.